use paragrapgh to answer number 32 ---**Testing Claims About Proportions**In Exercises 9-32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section).**10. M&Ms**Data Set 20 in Appendix B lists data from 100 M&Ms, and 8% of them are brown. Use a 0.05 significance level to test the claim of the Mars candy company that the percentage of brown M&Ms is equal to 13%.--- **HDTV Penetration**In a survey of 1500 households, it is found that 47% of them have a high-definition television (based on data from the Consumer Electronics Association). Use a 0.01 significance level to test the claim that fewer than half of all households have a high-definition television. Is the result from a few years ago likely to be valid today?(Note: The text contains no graphs or diagrams.)

In a survey of 1500 households, it is found that 47% of them have a high definition television. Let we define, p be the proportion of households that have high-definition television. Here we need to test claim that whether p is smaller than 50% or 0.50. The population proportion "p" is the parameter of interest so we use one sample proportion testing to test the claim about proportion. The null (H0) and alternative (H1) hypothesis in this are as follows; H0 : p ≥ 0.50 Vs H1 : p < 0.50 Since the alternative hypothesis contains sign "<" (smaller than), the test is the left tailed test. Let p^ be the sample proportion based on a sample of 1500 households. This gives, p^=0.47.The formula for calculating test statistic is given by, Z=p^-pp*(1-p)n ~N(0,1). Here in this example, we have n =1500, p = 0.50 and p^=0.47. By plugging these values in the formula we get, Z0=0.47-0.500.50*(1-0.50)1500Z0=-0.030.01291Z0=-2.3237Z0≈-2.32 The p-value is given by, P( Z < Z0) = P(Z < -2.32). This can be found using the excel command, "NORMSDIST(z)". Hence we get, p-value = 0.01. The significance level (α) is, 0.01. Hence the decision rule based on p-value is given by : "If p-value ≤ α then we reject null hypothesis otherwise we fail to reject null hypothesis." Here we get p-value = 0.01 = α = 0.01, hence we reject null hypothesis. Conclusion : There is sufficient evidence to support the claim that fewer than half of the households have high definition television.

Math

Statistics

32. HDTV Penetration In a survey of 1500 households, it is found that 47% of them have a high-definition television (based on data from the Consumer Electronics Association). Use a 0.01 significance level to test the claim that fewer than half of all households have a high- definition television. Is the result from a few years ago likely to be valid today?

32. HDTV Penetration In a survey of 1500 households, it is found that 47% of them have a high-definition television (based on data from the Consumer Electronics Association). Use a 0.01 significance level to test the claim that fewer than half of all households have a high- definition television. Is the result from a few years ago likely to be valid today?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.

Question

use paragrapgh to answer number 32

---

**Testing Claims About Proportions**

In Exercises 9-32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section).

**10. M&Ms**

Data Set 20 in Appendix B lists data from 100 M&Ms, and 8% of them are brown. Use a 0.05 significance level to test the claim of the Mars candy company that the percentage of brown M&Ms is equal to 13%.

---

**HDTV Penetration**

In a survey of 1500 households, it is found that 47% of them have a high-definition television (based on data from the Consumer Electronics Association). Use a 0.01 significance level to test the claim that fewer than half of all households have a high-definition television. Is the result from a few years ago likely to be valid today?

(Note: The text contains no graphs or diagrams.)

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